Polynomial chaos expansion of random coefficients and the solution of stochastic partial differential equations in the tensor train format

S Dolgov, BN Khoromskij, A Litvinenko… - SIAM/ASA Journal on …, 2015 - SIAM
We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics

J Giesselmann, C Lattanzio, AE Tzavaras - Archive for Rational Mechanics …, 2017 - Springer
We consider a Euler system with dynamics generated by a potential energy functional. We
propose a form for the relative energy that exploits the variational structure and we derive a …

Extended Lagrangian approach for the numerical study of multidimensional dispersive waves: Applications to the Serre-Green-Naghdi equations

S Tkachenko, S Gavrilyuk, J Massoni - Journal of Computational Physics, 2023 - Elsevier
In this paper we study two multidimensional nonlinear dispersive systems: the Serre-Green-
Naghdi (SGN) equations describing dispersive shallow water flows, and the Iordanskii …

Numerical solution of Navier–Stokes–Korteweg systems by Local Discontinuous Galerkin methods in multiple space dimensions

D Diehl, J Kremser, D Kröner, C Rohde - Applied Mathematics and …, 2016 - Elsevier
Compressible liquid–vapor flow with phase transitions can be described by systems of
Navier–Stokes–Korteweg type. They extend the Navier–Stokes equations by nonlinear …

Relaxation of the Navier–Stokes–Korteweg equations for compressible two‐phase flow with phase transition

J Neusser, C Rohde, V Schleper - International Journal for …, 2015 - Wiley Online Library
Summary The Navier–Stokes–Korteweg (NSK) system is a classical diffuse‐interface model
for compressible two‐phase flow. However, the direct numerical simulation based on the …

Fully resolved compressible two-phase flow: modelling, analytical and numerical issues

C Rohde - New trends and results in mathematical description of …, 2018 - Springer
Mathematical models for compressible two-phase flow of homogeneous fluids that occur in a
liquid and a vapour phase can be classified as either belonging to the class of sharp …

[PDF][PDF] Analysis and numerics of sharp and diffuse interface models for droplet dynamics

J Magiera, C Rohde - Droplet Dynamics Under Extreme Ambient …, 2022 - library.oapen.org
The modelling of liquid–vapour flow with phase transition poses many challenges, both on
the theoretical level, as well as on the level of discretisation methods. Therefore, accurate …

A relative entropy approach to convergence of a low order approximation to a nonlinear elasticity model with viscosity and capillarity

J Giesselmann - SIAM Journal on Mathematical Analysis, 2014 - SIAM
In this paper we study the dynamics of an elastic bar undergoing phase transitions. It is
modeled by two regularizations of the equations of nonlinear elastodynamics with a …

A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow

J Keim, HC Konan, C Rohde - arxiv preprint arxiv:2412.11904, 2024 - arxiv.org
We consider the two-phase dynamics of two incompressible and immiscible fluids. As a
mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the …

Deep-ultraviolet optoelectronic devices enabled by the hybrid integration of next-generation semiconductors and emerging device platforms

N Alfaraj - 2019 - repository.kaust.edu.sa
In this dissertation, the design and fabrication of deep-ultraviolet photodetectors were
investigated based on gallium oxide and its alloys, through the heterogeneous integration …